In the diagram below, what is the relationship between the number of
pentagons and the perimeter of the figure they form? Represent this relationship using a table, words, an equation, and a graph. Let x
=the number of
pentagons. Let y
=the perimeter of the figure.
22221 pentagon2 pentagons3 pentagons2
Represent the relationship using a table. Complete the table below.
Number of
Pentagons, x
Perimeter, y
Ordered Pair (x,y)
1
enter your response here
enter your response here
2
enter your response here
enter your response here
3
enter your response here
enter your response here
Number of Pentagons, x Perimeter, y Ordered Pair (x,y)
1 5 (1,5)
2 10 (2,10)
3 15 (3,15)
Multiply the number of
pentagons in each figure by
enter your response here
,
since all pentagons will have at least
▼
two
three
sides
that contribute to the perimeter of the combined figure. Then add
enter your response here
for
the
▼
two
three
unaccounted for sides on
the left and right ends of the combined figure to get the entire perimeter.
If we multiply the number of pentagons in each figure by 5, since all pentagons have 5 sides that contribute to the perimeter of the combined figure, we can then add 2 for the two unaccounted for sides on the left and right ends of the combined figure to get the entire perimeter.
y=
enter your response here (Simplify your answer. Type an expression using x as the variable.)
y = 5x + 2
To determine the relationship between the number of pentagons and the perimeter of the figure they form, we need to analyze the given information and complete the table.
In the diagram, it appears that there is one pentagon at the center, surrounded by 2 pentagons, and then surrounded by 3 pentagons. To find the perimeter, we need to add up the lengths of all the sides of the pentagons.
Based on the provided information, we can make the following observations:
- When there is 1 pentagon, the perimeter is unknown. We would need additional information about the size or length of the sides of the pentagon to determine the perimeter accurately. Therefore, we cannot fill in the values for this case.
- When there are 2 pentagons, we can identify that there is a shared side between the two pentagons. Assuming that each pentagon has five sides of equal length, the perimeter of the figure would be the sum of the lengths of 10 sides of the pentagon. However, without knowing the length of these sides, we cannot calculate the exact perimeter. We can still express it using a variable as: y = 10 * s, where s is the length of each side of the pentagon.
- When there are 3 pentagons, we observe that each new layer of pentagons adds a new outer side. Again assuming that each pentagon's sides are equal in length, there would be 15 sides (5 sides for the central pentagon, plus 10 sides for the outer layer). Similar to the previous cases, without the exact side length, we cannot calculate the precise perimeter. We can represent it using a variable as: y = 15 * s, where s is the length of each side of the pentagon.
Based on these observations, we can complete the table as follows:
Number of Pentagons, x | Perimeter, y | Ordered Pair (x,y)
1 | Unknown | (1, unknown)
2 | Unknown | (2, unknown)
3 | Unknown | (3, unknown)
Please note that without further information about the lengths of the pentagons' sides, we cannot provide exact numerical values for the perimeters.